Question

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 90 and standard deviation σ = 21. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)

(a) x is more than 60


(b) x is less than 110


(c) x is between 60 and 110


(d) x is greater than 140 (borderline diabetes starts at 140)

Answer 1

mean = 90

sd = 21

(a) P(x >60)

P(Z > -1.4286) = P(Z < 1.4286) = 0.9236

P(x >60) = 0.9236

(b) x is less than 110

P(z < 0.9524) = 0.8289

P(x < 110) = 0.8289

(c) x is between 60 and 110

P(-1.4286 < z < 0.9524) = P( z < 0.9524) - P(Z < -1.4286)

P( z < 0.9524) = 0.8289

P(Z < -1.4286) = 1- P (z < 1.4286) = 1- 0.9236 = 0.0764

P(-1.4286 < z < 0.9524) = 0.7525

P( x is between 60 and 110) = 0.7525  

(d) x is greater than 140 (borderline diabetes starts at 140)

P(z > 2.381) = 1- P(z < 2.381) = 1 - 0.9913 = 0.0087

P(x > 140) = 0.0087